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Welcome to the language barrier between physicists and mathematicians What is the lie algebra and lie bracket of the two groups? Physicists prefer to use hermitian operators, while mathematicians are not biased towards hermitian operators

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I have known the data of $\\pi_m(so(n))$ from this table I thought i would find this with an easy google search What is the fundamental group of the special orthogonal group $so (n)$, $n>2$

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The answer usually given is

To gain full voting privileges, The generators of so(n) s o (n) are pure imaginary antisymmetric n×n n × n matrices How can this fact be used to show that the dimension of so(n) s o (n) is n(n−1) 2 n (n 1) 2 I know that an antisymmetric matrix has n(n−1) 2 n (n 1) 2 degrees of freedom, but i can't take this idea any further in the demonstration of the proof

I'm not aware of another natural geometric object. A son had recently visited his mom and found out that the two digits that form his age (eg :24) when reversed form his mother's age (eg Later he goes back to his place and finds out that this whole 'age' reversed process occurs 6 times And if they (mom + son) were lucky it would happen again in future for two more times.

In case this is the correct solution

Why does the probability change when the father specifies the birthday of a son A lot of answers/posts stated that the statement does matter) what i mean is It is clear that (in case he has a son) his son is born on some day of the week. What is the probability that their 4th child is a son

(2 answers) closed 8 years ago As a child is boy or girl This doesn't depend on it's elder siblings So the answer must be 1/2, but i found that the answer is 3/4

What's wrong with my reasoning

Here in the question it is not stated that the couple has exactly 4 children U(n) and so(n) are quite important groups in physics